I always strugle with memorizing part. I am never able to reproduce word for word what I’ve learned or read, but I can put it into context and show my understanding pretty well. Here, with math theory, there is no alternative. I failed exams so many times only because of that vocal reproduction of learned theory that required word for word knowledge. I am having math exam on integral theory in 2 days and here I am sitting and lookin at screen. :)
You can do the exact same thing you mentioned with math. Theorems aren't arbitrary; there's a way they're derived. If you learn how the theorem comes to be, even if you can't remember exactly, you can often remember enough to come up with the theorem again.
I think the way you learn is the ideal. Knowing the context behind the facts you learn gives them worth, and the redundancy of being able to derive the fact from the context also makes it better integrated with the rest of your knowledge and easier to remember in the long term.
I totally agree with you, but I feel like with math theory there is always good chunk of knowledge that needs to be somehow inserted in your memory as is. That’s the most irritating part for me personally. If i find a way to overcome it or make it more accessible, I think I will enjoy math theory much much more. :)
I'm afraid it's just practice. Lots and lots of solving problems until the definitions, methods, and techniques are burned into your mind.
Once you have the background knowledge, everything is a lot simpler. Learn whether each theorem has an easy proof or a hard proof. If it has an easy proof, you can forget it (deriving it when you need to; an example is the contraction mapping theorem [1]). If it has a hard proof, you can forget it and look it up when you need to.
> I failed exams so many times only because of that vocal reproduction of learned theory that required word for word knowledge.
That sounds odd for college-level math courses (note that I am just a first year engineering undergrad and therefore possibly know nothing). Do you have oral part in your exams?
Yes. Talking with professor in front of you, and trying to pull everything out of my head is the hardest part. There I just don’t have enoigh time to sit down think about something and try to prove theorems on my own. And I’ve been on 2 faculties, more or less the same story on both. Forst had harder written test and assignments, second on which I’m currently has brutal oral part. I leave satisfied when i got the exam right, but the process of preparing it is fairly boring and fatiguing.
